3 problems

Let $\phi$ and $\psi$ be two almost strictly pure $t$-modules over $K$, and let $\phi\otimes\psi$ denote their tensor product. Choose a $K\{\tau\}$-basis of the corresponding $t$-m…

Let $K:=\mathbb{F}_{q}(\theta)$ be the rational function field, let $K_{v(\theta)}$ be its completion at the place $v(\theta)$, and let $K(t)_{v}$ and $K^{\mathrm{sep}}[t]_{v}$ be…

Let $K$ be a finite separable extension of $\mathbf{F}_q(t)$, let $A=\mathbf{F}_q[t]$, and let $K_\infty$ and $O_K$ denote the completions and the ring of integers used in the defi…